Functional Equations

Functional equations are mathematical equations where the unknowns are functions rather than specific values. They express relationships between these functions, often requiring us to find a function that satisfies the given equation. A common example is the equation \( f(x+y) = f(x) + f(y) \), which describes the additive property of a function. Solving functional equations can help uncover properties of functions in various fields, including mathematics, physics, and engineering. They often involve exploring the behavior of a function under specific operations and can lead to important insights in both theory and application.